New formulation of Horava-Lifshitz quantum gravity as a master constraint theory

TL;DR

This paper introduces a new formulation of non-projectable Horava-Lifshitz gravity using a master constraint algebra, resulting in a consistent canonical theory that maintains spatial diffeomorphisms and effectively enforces the Hamiltonian constraint.

Contribution

It presents a novel master constraint approach to non-projectable Horava-Lifshitz gravity, resolving previous constraint algebra issues and ensuring a consistent canonical framework.

Findings

Achieves a consistent first-class constraint algebra

Retains only spatial diffeomorphisms as gauge symmetry

Enforces the Hamiltonian constraint via the master constraint

Abstract

Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra scalar mode which can be problematic. A new formulation of non-projectable Horava-Lifshitz gravity, naturally realized as a representation of the master constraint algebra studied by loop quantum gravity researchers, is presented. This yields a consistent canonical theory with first class constraints. It captures the essence of Horava-Lifshitz gravity in retaining only spatial diffeomorphisms (instead of full space-time covariance) as the physically relevant non-trivial gauge symmetry; at the same time the local Hamiltonian constraint needed to eliminate the extra mode is equivalently enforced by the master constraint.